jud

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These are questions asked by jud

After this code:

g1 := PermutationGroup({[[1, 2]], [[1, 2, 3], [4, 5]]})

g1:=<(1, 2), (1, 2, 3)(4, 5)>

I can get a string "<(1, 2), (1, 2, 3)(4, 5)>". Could I use the string to restore the PermutationGroup with an elegant method?

lis := SearchSmallGroups('order' = 10 .. 100, 'soluble'): 
seq(DrawSubgroupLattice(SmallGroup(g), 'highlight' = CompositionSeries(SmallGroup(g))), g in lis[10 .. 20])

I want to see if these red nodes are present in each layer and connected at each level, so I need to detect a large number of images. But if I put them in the same row, these images will be very small and I have to zoom in one by one with the mouse to see them. How can I set the size of these images?

ps:I'm currently using my eyes to determine if these red nodes are present at each layer and connected at each level, and I'd be happy if there was code to do this

with(GroupTheory):

st := time();
RightCosets(SymmetricGroup(10), SymmetricGroup(11));
time() - st;

0.047

Note GroupOrder(SymmetricGroup(11)) is 39916800. It is a very large group. This seems unimaginable to me. Can I know how maple does it?

As we know, when every Gi is normal in G, then the series is called a normal series:

cs := CompositionSeries(DihedralGroup(8))

We can draw it:

DrawSubgroupLattice(DihedralGroup(8), labels = ids, highlight = cs)

And all Gi is normal in G:

IsNormal~(cs, DihedralGroup(8))

[true, true, true, true, true]

But why type(cs, 'NormalSeries') will get false.. It is a bug or do I have a misunderstanding?

When The subgraph is too many, the label will hide automatically. Such as:

DrawSubgroupLattice(SmallGroup(200, 31), labels = ids)